How to make part of the model not be subdivided？
Same example:


Becomes:


The solution is:
1. Select the edges you don't want to be subdivided



In the right bar (Press N to show it) set the "Mean Crease" value to 1 (it sets how much the selected edges don't react to subdivision smoothness Edit: note that the face is still subdivided but the subfaces created by subdivision mantain the original position. No smoothness.). They'll become violet.

Turn back to Edit Mode and enjoy